Pointing device with reduced component count

ABSTRACT

A signal processing system for a strain-gauge pointing device has a reduced parts count and permits the use of relatively inexpensive low-tolerance components. The system can process signals from two or three or more strain gauges, permitting additional inputs by users without a linear increase in the number of signal processing components. The system employs an RC network to develop an offset for the signal to be provided to an analog-to-digital converter. The system performs each measurement twice, once with a particular excitation polarity and again with the opposite excitation polarity, which permits correction for drift and temperature instability.

This is a divisional of Ser. No. 08/708,048, filed Aug. 30, 1996, nowU.S. Pat. No. 5,874,938 which is herein incorporated by reference.

The invention relates generally to user input devices for personalcomputers, and relates more specifically to a sensitive and accuratesignal processing path for a small-signal strain-gauge user pointingdevice having low power consumption and reduced component count. Thesignal processing path offers its benefits in many other dataacquisition applications, however, including systems using strain gaugesensors.

BACKGROUND OF THE INVENTION

The first decades of the computer revolution were focused on theprocessor. Now that processors are arbitrarily small, arbitrarily fast,and inexpensive, it has become possible to make a shift away from aworld containing a small number of large, line-powered non-mobilecomputer systems, to a world in which lots of people have computers andthe computers are small, portable, and battery powered. Graphical userinterfaces are now common, representing a shift in the user interfaceaway from the character-oriented user input devices and displays of thepast. But at the same time that graphical user interfaces have becomecommonplace, the personal computer has also been shrinking. Formerly thesize of the processor and associated electronics was so great that therewas little reason to try to miniaturize anything else. Nowadays thedesigner of a personal computer faces a design environment in which theprocessor is quite small, and the limiting factors for package size arethe dimensions of the screen, the keyboard and pointing device, and thebattery. The screen, keyboard, and battery have yielded to theengineers' energies to the extent possible at the present time, leavingthe pointing device as one of the few remaining targets ofminiaturization efforts. The classic track ball and mouse have too manymoving parts and are too bulky for today's smallest computers, leavingthe force-sensitive joystick as a very popular pointing device for userinput.

The force-sensitive joystick presents itself to the consumer as aresilient button in the lower center of the keyboard, looking much likea pencil eraser. The button (60 in FIG. 1) connects to a small straingauge 61 that is hidden from the view of the consumer. In a typicalprior-art embodiment the strain gauge 61 is a four-wire device as shownin FIG. 1, defined by the variable resistors 62-65 in FIG. 1. Anexcitation signal (power and ground in FIG. 1) is applied to the straingauge. Two of the resistors 62-63 define a voltage divider with anoutput 66 indicative of vertical displacement of the pointing device.The remaining resistors 64-65 define a voltage divider with an output 67indicative of horizontal displacement of the pointing device. One maythink of these resistors as comprising a potentiometer, since the usualresult of displacement the pointing device is that one resistorincreases its resistance and the other resistor decreases itsresistance. As a general matter the result is that the potentialmeasurable at the output is monotonically related to the displacement ofthe pointing device.

At this point the mechanical engineer's duties are completed and theelectrical engineer must find a way (box 68 in FIG. 1) to process thetwo outputs, to convert them to digital values, and to make themavailable to software on digital data lines 73-74 for processing. Insoftware the absolute position of the button 60 is converted to avelocity value, which in practical terms means that force is convertedto speed of the cursor, a conversion that is well known to those in theart and plays no part in the present invention. The signal processingcircuitry 68 will typically contain amplifiers and analog-to-digitalconverters such as amplifiers 69-70 and A/D converters 71-72.

The design of the signal processing circuitry is not easy. One enormousdifficulty comes from the fact that the resistors 62-65 don't vary muchin value in response to the user input at button 60. The voltage changedetectable at 66 or 67 is quite subtle, on the order of 300 to 500microvolts. This requires a high gain in the amplifiers 69-70. Anotherconstraint is that the analog-to-digital converters (A/D converters)available for use by the engineer present a tradeoff of cost versusdynamic range. An eight-bit A/D converter is not very expensive, but ahigher-resolution A/D converter is more expensive by at least an orderof magnitude. This means that one must find a way to get by with aninexpensive A/D converter. But the dynamic range of the A/D converter isnot very great, and the necessarily highly amplified signals from thehigh-gain amplifiers 69-70 are likely to swing beyond the end points ofthe input range of the A/D converters and into saturation at the powerrails.

The hard times presented by having to do analog-to-digital conversionson small-amplitude signals lead to desperate measures. FIG. 2 shows oneprior-art approach to the problem, in which only one of the two axes ofthe pointing device is shown for clarity. Line 78 carries the signalfrom voltage divider 62-63 to differential amplifier 80, where it isamplified and provided to analog-to-digital converter 71. When the firstmeasurement is made (for example, upon power-up of the system), thesystem is powered up through switch 172 controllable by themicrocontroller, and a programmable potentiometer 76 is used to “zero”the signal at 83 to the A/D converter. Potentiometer 76 is used withresistors 72, 122 and 123 to form a voltage divider which defines aWheatstone bridge with voltage divider 62-63. Under control ofmicrocontroller 81, the potentiometer 76 is adjusted to give a “zero” atthe input to the A/D converter. The programmed setting of thepotentiometer is noted and stored if necessary within themicrocontroller 81.

It will be appreciated that the programmable potentiometer, togetherwith its applied potentials, may be thought of as a digital-to-analog(D/A) converter. The microcontroller 81 is preferably a single-chipcontroller with a built-in A/D converter, but could more generally beany processor executing a suitable stored program.

The term “zero” in this context is in fact an arbitrary term, and infact the potentiometer is used to cause the signal to the A/D converterto rest at some level that is convenient for measurement. In the systemof FIG. 2 the output of the op amp swings between 0 and 5 volts, inwhich case the convenient value is about 2.5 volts, selected because theop amp is linear in that range and the dynamic range is centered aboutthat value. Thus, 2.5 volts is rather arbitrarily defined as “zero” or“null” for purposes of the subsequent A/D conversion. At later timeswhen it is desired to know the position of the pointing device, theswitch 172 is again turned on, and vertical deflection of the button 60changes the values of resistors 62-63. The changed voltage at 78 yieldsa difference with the potentiometer wiper voltage at 79, and thus anonzero signal at 83. This signal is converted to digital data for line82.

It will be appreciated that the arrangement of FIG. 2 does function. Butit will be appreciated by those skilled in the art that the arrangementof FIG. 2 is but one of at least two signal processing channels. Thetotal component count includes not one but two programmablepotentiometers, as well as expensive and high-precision components(resistors, capacitors, and amplifiers) elsewhere in the channels.

It is desirable to have a signal processing system for strain-gaugepointing devices having a reduced parts count, and permitting the use ofrelatively inexpensive low-tolerance components. It is likewisedesirable to have a signal processing system in which the components canprocess signals from two or three or more strain gauges, permittingadditional inputs by users without a linear increase in the number ofsignal processing components.

SUMMARY OF THE INVENTION

A signal processing system for a strain-gauge pointing device has areduced parts count and permits the use of relatively inexpensivelow-tolerance components. The system can process signals from two orthree or more strain gauges, permitting additional inputs by userswithout a linear increase in the number of signal processing components.The system employs an RC network to develop an offset for the signal tobe provided to an analog-to-digital converter. The system performs eachmeasurement twice, once with a particular excitation polarity and againwith the opposite excitation polarity, which permits correction fordrift and temperature instability.

DESCRIPTION OF THE DRAWING

The invention will be described with respect to a drawing in severalfigures, of which:

FIG. 1 is a prior-art generalized schematic of a strain-gauge pointingdevice;

FIG. 2 shows in some detail the signal processing circuitry in aprior-art system;

FIG. 3 shows in schematic form a signal processing circuit in accordancewith the invention; and

FIG. 4 shows in schematic form a signal processing circuit in accordancewith a second embodiment of the invention.

DETAILED DESCRIPTION

FIG. 3 shows an embodiment of a signal processing circuit in accordancewith the invention. The output at 84 from a resistor voltage divider isamplified by high-gain amplifier 85 and provided at 83 to ananalog-to-digital converter omitted for clarity in FIG. 3. (FIG. 2 showshow a microcontroller 81 with an A/D converter 71 might be employed toreceive the signal at 83.) Again referring to FIG. 3, an offset isprovided to bring the signal at 84 into the center of the dynamic rangeof the A/D converter and/or the center of the output range of theamplifier, and this is accomplished by capacitor network 87-88 andcharging resistors 90-91 under control of the microcontroller as willnow be described.

When the system is first powered up, the excitation signal is suppliedto the voltage divider of the strain gauge and the developed analogsignal at 84 is provided to the differential op amp 85. The other inputto the amplifier 85 is from the offset circuitry just mentioned. Theswitched-power line 95 is grounded (by a push-pull driver omitted forclarity in FIG. 3) and the discharge FET 89 is switched on by dischargecontrol line 94, again under control of the microcontroller. This bleedsoff nearly all the charge on the capacitors 87-88. Then the dischargeFET 89 is turned off, and the push-pull driver for the switched powerline 95 is driven to operating voltage. Capacitors 87-88 quickly chargeup and the voltage at 98 is about half of the operating voltage. Ameasurement is made at the A/D converter to determine whether the signalat 83 is null (zero). (It will be recalled from the earlier discussionthat “null” means some arbitrary value in the center of the linear rangeof the system and in the center of the dynamic range of the system; thesystem of FIG. 3 swings between 0 and 5 volts so “null” is definedarbitrarily as 2.5 volts.) If the signal is at a null, then theoffset-coarse line 93 is driven (by a tri-state driver, again omittedfor clarity in FIG. 3) under microcontroller control to attempt to nullthe signal at 83. Coarse-adjust resistor 90 forms an RC network and thetime constant determines what duration of coarse-offset signal isrequired to accomplish a desired potential at 98. The coarse adjustmentcan be upward; or downwards, and because the drivers are tri-state, thecoarse adjustment and fine adjustment do not interfere with each other.The resistors 90-91 and capacitors 87-88 and the associated circuitrymay be thought of as a digital-to-analog (D/A) converter, albeit not aconverter with much linearity.

The clock speed of the microcontroller places a granularity on theduration of a coarse-adjust signal. For this reason, a second resistor91 (defining a much longer time constant with respect to the capacitors)is provided. Under microprocessor control a fine-offset line 92 isdriven by a tri-state driver to achieve a fine adjustment to the voltageat 98.

The voltage at 98 is isolated by unity-gain amplifier 86 and provided tothe other of the two inputs of differential amplifier 85. Aftersufficient microcontroller current bursts through coarse and fine-adjustresistors 90-91, the voltage at 98 closely approximates that at 84 andthe output 83 is null (zero) (or center of the dynamic range of the A/Dconverter and/or the amplifier).

After such nulling of the signal processing path, subsequent deflectionsof the button 60 give rise to changes in the signal 83 and are detectedby the A/D converter and made available to software for processing as inthe prior art.

The circuitry described thus far in FIG. 3 offers a substantialreduction in parts count and parts cost as compared with the prior-artapproach of FIG. 2. An expensive and bulky programmable potentiometerhas been replaced with less expensive and less bulky components. Afurther advantage is that the signal processing data path in the systemaccording to the invention has a wide dynamic range in comparison to thesystem of FIG. 2, since the RC network that develops the offset has awider range, electrically, than the potentiometer arrangement of FIG. 2.

Additional aspects of the system of FIG. 3 will now be described whichpoint up further advantages over the prior art. It will be noted thatthe excitation signals for the strain gauge are applied throughtri-state drivers 104-107. One consequence of the use of the drivers104-107 is that the voltage divider 64-65 has an output that is tieddirectly to the output of voltage divider 62-63. This is in directcontrast to the prior-art approach of FIGS. 1 and 2 in which eachvoltage divider has its own distinct signal processing path, its owncorresponding programmable potentiometer, and its own analog-to-digitalconverter. In the system of FIG. 3, it is possible to energize onlydrivers 104 and 106 (thus energizing axis channel 100) on the one hand,or to energize only drivers 105 and 107 (thus energizing axis channel101). When one of the channels 100 or 101 receives its excitation, thenthe signal processing path 124 measures the deflection in that axis. Inthis way a single signal processing path 108 is able to collect datafrom a number of axes, and while the number of channels 100, 101 isshown as two, the system may be expanded to handle more channels inparallel with channels 100, 101 in FIG. 3. As a result, a substantial(nearly two to one or more) savings in component count and cost isenjoyed. Only one signal processing path 124 is needed and only one A/Dconverter (omitted for clarity in FIG. 3) is needed. It will beappreciated that the outputs of the drivers 104-107 are tristate, thatis, that each source of excitation potential is capable of being set toa high impedance to permit some other voltage divider to be measured.

While the points made thus far show substantial advantages over theprior art, further advantages will be apparent to those skilled in theart, as will now be described. It will be noted that the drivers 104-107are tri-state drivers, each containing switches 102-103 (shown in driver104). These switches are an integral part of a typical microcontroller,which means that they do not contribute to the parts count, and thus donot contribute to assembly cost. The switches are controlled through themicrocontroller by drive lines 108-111. An important capability may nowbe seen. It is possible, under microcontroller control, to excite eachvoltage divider with either of two polarities of excitation potential.

In an exemplary embodiment, upon power-up the X excitation 108 isprovided, giving working voltage at the top of voltage divider 64-65 andground at the bottom of the divider. The signal at 84 is indicative ofthe at-rest X position of the pointer button 60. The microprocessorzeroes the capacitors 87-88 by grounding 95 and energizing 94, and thenapplies bursts of current as needed at 93 and then 92 to integrate to apotential at 98 that nulls the signal at 84. Careful note is made,within the microcontroller, of the burst durations that were needed todevelop the null. (Those skilled in the art will appreciate that it isdesirable for the resistor 91 and the resistor 90 to have a ratio ofslightly less than 16 to 1.)

Importantly, what happens next (under microcontroller control) is thatthe X excitation 108 is turned off and the X excitation 109 is nowturned on. The voltage divider is now receiving an excitation signal ofopposite magnitude. The signal at 84 is different now (except in theexceedingly unlikely event of the two resistors 64-65 being exactlyequal in value) and a different set of burst durations at lines 92-93 isfound to null the output at 83. These durations are also noted for laterreference, and the difference in the (nearly zero) nulled outputs at 83(in response to the two different excitation polarities from lines 108and 109) is noted.

What has been described up to this point is the calibration uponpower-up for one axis 100. The calibration is repeated for each otheraxis such as axis 101 in FIG. 3. For each axis, what is noted within thememory of the microcontroller are the following three numbers: the burstduration that (nearly) nulled the signal with one excitation polarity(call this A), the burst duration that (nearly nulled the signal withthe other excitation polarity (call this B), and the difference betweenthe two (near) nulls (call this C).

In the time after power-up, when the pointing device is being used, itis necessary from time to time to measure the pointing devicedeflection. The exemplary procedure for this measurement is as follows.First, the excitation 108 is turned on. The offset circuitry isprogrammed with bursts as defined by A. The output at 83 is measured(call this D). Then the excitation 109 is turned on. The offsetcircuitry is programmed with bursts as defined by B. The output at 83 ismeasured (call this E). Then the difference between these two readingsis calculated in the microcontroller (this is D-E). Finally thedifference between the two near-nulls that was determined duringinitialization (C) is subtracted. The result is a number indicative ofthe button displacement. Expressed as a formula the result is ((D-E)-C).

Those skilled in the art will appreciate that the procedure justdescribed, which involves using two polarities of excitation duringsetup and two polarities of excitation during measurement, permits theuse of relatively inexpensive electronic components in the signalprocessing data path. Drift, poor tolerance, and many other factors thatmight otherwise lead to systematic error in measurement of the buttondeflection are corrected and eliminated.

It might be thought that the need to do two excitations and A/Dmeasurements for each position measurement would take too long. Butactual testing shows that with inexpensive 8-bit A/D converters andother components, and with modest clock speed for the microcontroller,it is possible to perform a single data collection in under 250microseconds, and thus the two measurements for a single axis in doublethat time, or under 500 microseconds.

In one embodiment of the invention, it is desirable to have a ratio ofslightly less than sixteen to one for the values of the resistors 90 and91. The reason for this will be clear to those skilled in the art,namely that the current burst durations for the two resistors may thenbe expressed in binary and the bit patterns concatenated. The high-orderfour bits of an eight-bit byte can convey the burst duration for thecoarse adjust time interval through resistor 90, while the low-orderfour bits of the byte can convey the current burst duration for the fineadjust time interval through resistor 91. Importantly, there is norequirement that the ratio of the resistors be exactly sixteen to one.What is needed is that the offset potential developed in the capacitors87-88 be repeatable (and without large gaps) with respect to the digitalinput. During the power-up initialization, the offset potential isderived through successive approximations, while during subsequentmeasurements the offset potential is simply developed as quickly aspossible. The coarse offset current burst might typically have aduration of zero to sixteen microseconds (a granularity determined bythe clock rate of the microcontroller) and the fine offset current burstmight likewise have a duration of zero to sixteen microseconds. The twobursts may be performed one after the other (which only takes 32microseconds in this example) or, if time were critical, the burstscould be overlapping in time, for example, by charging the capacitorsthrough the two resistors simultaneously for part of the time. Stateddifferently, if the ratio is slightly less than sixteen to one, thenthere is no danger that the effect resulting from a single time unitwith the coarse adjust resistor will exceed the effect resulting from afull sixteen time units with the fine adjust resistor.

In another embodiment, it is considered desirable to have more thaneight bits of D/A, for example about nine bits. In this case, there maybe five bits of coarse adjustment and another five bits of fineadjustment, concatenated to form a ten-bit integer with a theoretical1024 steps. In practice the actual number of steps giving rise to usefulanalog outputs will be somewhere between 512 and 1024 steps. The ten-bitinteger is stored in a sixteen-bit word. In this embodiment the ratio ofthe resistors is slightly less than 32. FIG. 4 shows an alternativeembodiment of the system according to the invention. The offset andamplifier section 108 of FIG. 3 is replaced with the circuitry of FIG. 4in this embodiment. Two operational amplifiers are used, just as in FIG.3, but their sequence is reversed. The voltage divider output 84 passesthrough unity-gain amplifier 120 for isolation and then to an input ofdifferential amplifier 121. The offset potential developed withincapacitors 87, 88 is applied to the other input of differentialamplifier 121. Amplifier 121 thus provides both a numerical subtractionof its two inputs and also provides the high gain required to amplifythe small signal at 84 for the A/D converter (omitted for clarity inFIG. 4).

While the invention is described in connection with a pointing device,those skilled in the art will appreciate that the signal processingsystem described herein is applicable to many other applications. Anyother application using a strain gauge, for example a scale, can use thesignal processing system described herein with the same benefitsincluding the ability to use inexpensive parts instead of high-toleranceparts, and the ability to minimize the parts count.

Those skilled in the art will have no difficulty devising obviousvariations of the above-described invention, all of which areencompassed by invention as defined in the claims which follow.

What is claimed is:
 1. A pointing device comprising: a processor; afirst voltage divider having first and second ends and having an outputthe potential of which is monotonically related to applied force in afirst axis of the pointing device; a first source of excitationpotential connected to the first voltage divider and switchable betweenfirst and second polarities thereof under control of the processor; asecond voltage divider having first and second ends and having an outputthe potential of which is monotonically related to applied force in asecond axis of the pointing device; a second source of excitationpotential connected to the first voltage divider and switchable betweenfirst and second polarities thereof under control of the processor; thefirst and second sources of excitation potential each capable of beingswitched to a high-impedence state; a digital-to-analog convertercontrolled by the processor and having an analog output; ananalog-to-digital converter receiving as its input signals indicative ofthe first voltage divider output, the second voltage divider output, andthe digital-to-analog converter output.
 2. A method of measuring theposition of a pointing device in two axes, the pointing device of a typehaving a first voltage divider having first and second ends and havingan output the potential of which is monotonically related to appliedforce in a first axis of the pointing device, the pointing devicefurther having a second voltage divider having first and second ends andhaving an output the potential of which is monotonically related toapplied force in a second axis of the pointing device, the pointingdevice further having a digital-to-analog converter having an analogoutput, the pointing device further having an analog-to-digitalconverter receiving as its input signals indicative of the first voltagedivider output, the second voltage divider output, and thedigital-to-analog converter output, said method comprising the stepsfirst initializing, first measuring, second initializing, and secondmeasuring: the first initializing step comprising the steps of: applyingan excitation potential of a first polarity to the first voltage dividerand applying no potential to the second voltage divider; causing thedigital-to-analog converter to have an output such that the input signalto the analog-to-digital converter is within its dynamic range, defininga first potential as the potential measured by the analog-to-digitalconverter, and defining a first digital value as the input to thedigital-to-analog converter; applying an excitation potential of asecond polarity to the first voltage divider and applying no potentialto the second voltage divider; causing the digital-to-analog converterto have an output such that the input signal to the analog-to-digitalconverter is within its dynamic range, defining a second potential asthe potential measured by the analog-to-digital converter, and defininga second digital value as the input to the digital-to-analog converter;the first measuring step comprising the steps of: applying theexcitation potential of the first polarity to the first voltage dividerand applying no potential to the second voltage divider; providing thefirst digital value to the digital-to-analog converter, and defining athird potential as the potential measured by the analog-to-digitalconverter; applying the excitation potential of the second polarity tothe first voltage divider and applying no potential to the secondvoltage divider; providing the second digital value to thedigital-to-analog converter, and defining a fourth potential as thepotential measured by the analog-to-digital converter; the secondinitializing step comprising the steps of: applying an excitationpotential of a first polarity to the second voltage divider and applyingno potential to the first voltage divider; causing the digital-to-analogconverter to have an output such that the input signal to theanalog-to-digital converter is within its dynamic range, defining afifth potential as the potential measured by the analog-to-digitalconverter, and defining a third digital value as the input to thedigital-to-analog converter; applying an excitation potential of asecond polarity to the second voltage divider and applying no potentialto the first voltage divider; causing the digital-to-analog converter tohave an output such that the input signal to the analog-to-digitalconverter is within its dynamic range, defining a sixth potential as thepotential measured by the analog-to-digital converter, and defining afourth digital value as the input to the digital-to-analog converter;the second measuring step comprising the steps of: applying theexcitation potential of the first polarity to the second voltage dividerand applying no potential to the first voltage divider; providing thethird digital value to the digital-to-analog converter, and defining aseventh potential as the potential measured by the analog-to-digitalconverter; applying the excitation potential of the second polarity tothe second voltage divider and applying no potential to the firstvoltage divider; providing the fourth digital value to thedigital-to-analog converter, and defining an eighth potential as thepotential measured by the analog-to-digital converter; evaluating afunction of the first, second, third, and fourth potentials, the outputof the function indicative of the applied force on the device in thefirst axis; and evaluating a function of the fifth, sixth, seventh, andeighth potentials, the output of the function indicative of the appliedforce on the device in the second axis.
 3. A signal processing systemcomprising: a processor; a first voltage divider having first and secondends and having an output the potential of which is monotonicallyrelated to a first physical value; a first source of excitationpotential connected to the first voltage divider and switchable betweenfirst and second polarities thereof under control of the processor; asecond voltage divider having first and second ends and having an outputthe potential of which is monotonically related to a second physicalvalue; a second source of excitation potential connected to the firstvoltage divider and switchable between first and second polaritiesthereof under control of the processor; the first and second sources ofexcitation potential each capable of being switched to a high-impedencestate; a digital-to-analog converter controlled by the processor andhaving an analog output; an analog-to-digital converter receiving as itsinput signals indicative of the first voltage divider output, the secondvoltage divider output, and the digital-to-analog converter output.
 4. Amethod of measuring first and second physical values using a sensor ofthe type having a first voltage divider having first and second ends andhaving an output the potential of which is monotonically related to thefirst physical value, the device further having a second voltage dividerhaving first and second ends and having an output the potential of whichis monotonically related to the second physical value, the devicefurther having a digital-to-analog converter having an analog output,the device further having an analog-to-digital converter receiving asits input signals indicative of the first voltage divider output, thesecond voltage divider output, and the digital-to-analog converteroutput, said method comprising the steps first initializing, firstmeasuring, second initializing, and second measuring: the firstinitializing step comprising the steps of: applying an excitationpotential of a first polarity to the first voltage divider and applyingno potential to the second voltage divider; causing thedigital-to-analog converter to have an output such that the input signalto the analog-to-digital converter is within its dynamic range, defininga first potential as the potential measured by the analog-to-digitalconverter, and defining a first digital value as the input to thedigital-to-analog converter; applying an excitation potential of asecond polarity to the first voltage divider and applying no potentialto the second voltage divider; causing the digital-to-analog converterto have an output such that the input signal to the analog-to-digitalconverter is within its dynamic range, defining a second potential asthe potential measured by the analog-to-digital converter, and defininga second digital value as the input to the digital-to-analog converter;the first measuring step comprising the steps of: applying theexcitation potential of the first polarity to the first voltage dividerand applying no potential to the second voltage divider; providing thefirst digital value to the digital-to-analog converter, and defining athird potential as the potential measured by the analog-to-digitalconverter; applying the excitation potential of the second polarity tothe first voltage divider and applying no potential to the secondvoltage divider; providing the second digital value to thedigital-to-analog converter, and defining a fourth potential as thepotential measured by the analog-to-digital converter; the secondinitializing step comprising the steps of: applying an excitationpotential of a first polarity to the second voltage divider and applyingno potential to the first voltage divider; causing the digital-to-analogconverter to have an output such that the input signal to theanalog-to-digital converter is within its dynamic range, defining afifth potential as the potential measured by the analog-to-digitalconverter, and defining a third digital value as the input to thedigital-to-analog converter; applying an excitation potential of asecond polarity to the second voltage divider and applying no potentialto the first voltage divider; causing the digital-to-analog converter tohave an output such that the input signal to the analog-to-digitalconverter is within its dynamic range, defining a sixth potential as thepotential measured by the analog-to-digital converter, and defining afourth digital value as the input to the digital-to-analog converter;the second measuring step comprising the steps of: applying theexcitation potential of the first polarity to the second voltage dividerand applying no potential to the first voltage divider; providing thethird digital value to the digital-to-analog converter, and defining aseventh potential as the potential measured by the analog-to-digitalconverter; applying the excitation potential of the second polarity tothe second voltage divider and applying no potential to the firstvoltage divider; providing the fourth digital value to thedigital-to-analog converter, and defining an eighth potential as thepotential measured by the analog-to-digital converter; evaluating afunction of the first, second, third, and fourth potentials, the outputof the function indicative of the first physical value; and evaluating afunction of the fifth, sixth, seventh, and eighth potentials, the outputof the function indicative of the second physical value.